POLICE were last night probing a theory that Oscar Pistorius battered girlfriend Reeva Steenkamp over the head with a cricket bat, then shot her dead.

They have sent a blood-stained bat recovered from the Paralympic legend’s home in Pretoria, South Africa, for forensic examination.

The tests will determine whether it caused skull damage suffered by the stunning 29-year-old model.

In a separate development yesterday, it emerged that officers are examining whether Pistorius, 26, may have been under the influence of steroids at the time of the killing.

Detectives are also looking into the possibility that the sprinter shot Miss Steenkamp over her “close friendship” with South African rugby player Francois Hougaard.

Pistorius, six-times Paralympic gold medal winner and the only double amputee to complete in the Olympics, is expected to make a bail application tomorrow.

The athlete, dubbed Blade Runner, is being held at Pretoria’s Brooklyn police station following last week’s shooting at his apartment. He denies murdering Reeva and his family insists last week’s shooting was a tragic accident.

But yesterday Johannesburg’s City Press newspaper reported the discovery of the cricket bat. It quoted an insider: “There was lots of blood on the bat. Forensic tests will show whose blood it was.”

Officers are apparently unsure whether the bat was used to strike her intentionally or if it was used to break down the door of a toilet she is said to have hidden inside.

They are also considering the possibility that Reeva, a law graduate, used the weapon against Pistorius in self-defence.

Claiming three well-placed sources, City Press said police have ruled out a suggestion by the Pistorius family that she could have been mistaken for an intruder.

Police crime scene tape marks off the Pretoria home of South African "Blade Runner" Oscar Pistorius

There was lots of blood on the bat. Forensic tests will show whose blood it was.

Johannesburg’s City Press newspaper

They found no evidence of a forced entry but say bedclothes were crumpled, suggesting the couple both slept in the bed that night. Forensic officers also found one gun cartridge in the bedroom, suggesting he may have fired at her there before chasing her into the adjacent toilet.

The source said: “The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and locked herself in the toilet.

“She was doubled over because of the pain. He fired three more shots. She probably covered her head, which is why the bullet also went through her hand.”

Police have also insisted on toxicity tests on the runner’s blood in case he suffered an aggressive reaction to steroids. The drugs, illegally taken by some athletes, have been known to spark towering “roid rages” among users.

Rumours also emerged over the weekend about Miss Steenkamp and Springbok star Hougaard, 24. He pulled out of a game for his Vodacom Bulls side on Friday as speculation grew about his relationship with the FHM model.

Nelson Mandela aide Zelda la Grange wrote on Twitter. “Have you heard rumours about a rugby player alleged to be involved somehow? ”

Hougaard’s agent Lorinda Voges said: “This is still an ongoing investigation. This whole sad ordeal has got nothing to do with him.” Meanwhile Pistorius’s best friend Justin Divaris told how he received a distraught phone call from the star moments after the shooting.

Mr Divaris rushed to the scene, to find it sealed off by police. But he described seeing Reeva covered in blankets and towels. Her father Barry said yesterday he was struggling “to find some reason why this happened to our lovely daughter”.

In a moving interview, he said he bore Pistorious no animosity, adding: “We just need to find some answers. Reeva was the most beautiful, kind girl in the world.”

Pistorius’s spokesman Peet van Zyl said the star had received “overwhelming support” from fans.

And his grandmother Gertie Pistorius, 89, said: “I know it was a mistake anybody can make.”

Prosecutors are set to oppose a bail application tomorrow and will pursue upgraded charges of premeditated murder.